Example 17 - Solve -5 <= 5 - 3x/2 <= 8 - Chapter 6 CBSE - Examples

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  1. Chapter 6 Class 11 Linear Inequalities
  2. Serial order wise
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Example 17 Solve – 5 ≤ 5 − 3𝑥﷮2﷯ ≤ 8. – 5 ≤ 5 − 3𝑥﷮2﷯ ≤ 8 Multiplying 2 all sides (Eliminating 2) – 5 × 2 ≤ 5 – 3x ≤ 8 × 2 –10 ≤ 5 – 3x ≤ 16 Subtracting 5 all sides (Eliminating 5) –10 – 5 ≤ 5 – 3x – 5 ≤ 16 – 5 –10 – 5 ≤ 5 – 3x – 5 ≤ 16 – 5 – 15 ≤ –3x ≤ 11 Dividing 3 all sides (Eliminating 3) −15﷮3﷯ ≤ −3𝑥﷮3﷯ ≤ 11﷮3﷯ -5 ≤ −𝑥 ≤ 11﷮3﷯ Since x is negative, we multiply both sides by -1 & change the signs (– 1) × (-5) ≥ (–1) × (–x) ≥ (–1) × ( 11﷮3﷯) 5 ≥ x ≥ −11﷮3﷯ ⇒ −11﷮3﷯ ≤ x ≤ 5 Thus, x is a real number which is less than or equal to 5 and greater than or equal to −11﷮3﷯ Hence, x ∈ −𝟏𝟏﷮𝟑﷯, 5﷯ is the solution

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